Quark condensate in a magnetic field

We study the dependence of quark condensate $\mathrm{\Sigma }$ on an external magnetic field. For weak fields, it rises linearly with the field. Pion mass and residue are also shifted so that the Gell-Mann - Oakes - Renner relation is satisfied. In the strong field region, $\mathrm{\Sigma }(H)\propto (eH{)}^{3\mathrm{/}2}$.